APPENDIX A 



of azimuth may be substituted for those of altitude. The former was the method 

 adopted in determining the longitude of Ssumao. 



This proceeding is, on the whole, the best that can be followed in exploration, 

 next to that of occultations, which necessitate the carrying of a powerful telescope. 

 It is superior to those of lunar altitudes and lunar distances by the sextant, as the 

 value of the latter depends upon taking several series east and west to eliminate 

 the error of centring Nevertheless, it must be borne in mind that every error of 

 observation being multiplied by thirty in the result, an approximation only of from 

 7' to 10' can be counted on with the small theodolite at my disposal. With a 

 large theodolite repeater M. Caspari was able to obtain an approximation of 2', 

 but such a result can only be regarded as exceptional. 



This want of precision being recognised, I was unable to bring to bear the 

 same exactness of correction on my longitudes as on my latitudes. I can, however, 

 affirm that each point entered in the foregoing list lies within a settled zone of 

 between 15' and 20' in breadth. It is important, while bearing in mind the vast 

 tracts of wholly unexplored country involved, to admit a certain, even if exaggerated, 

 margin for error. This importance naturally decreases in proportion as the divergence 

 in the observations diminishes, and disappears if it is a matter of correcting a 

 march of a few days only. 



By a systematic comparison of my estimated with my observed latitudes, I can 

 show the amount of reliance to be placed on my reckoning. In a period of 

 travel extending over two months the error never amounted to more than 

 between 7' and 10'. As Francis Gamier based all his longitudes on observations 

 of lunar distances with the sextant, their approximation is not closer. For the 

 positions of Tali and Ssumao, the two fundamental points of my map, through 

 which places he also passed, I have therefore judged it the most reasonable 

 process to take the mean between our respective observed longitudes, using my 

 value for error in the estimated longitudes. 



From all which deliberations I am in a position to assume that the error in 

 the longitudes of my map does not exceed 4' to 5' — at any rate as far as Tali-Fou. 

 After the loss of my theodolite I had to rely on my estimation ; yet, on comparing 

 my journey with that of Captain Gill to Atentse, and with the geodesic survey of 

 India, I was able on arrival in Assam to check my calculations, and to correct the 

 intermediate points in proportion. When we reached Khamti, after three months' 

 travel through the most arduous country, I was only 6' out in latitude and 5' in 

 longitude from the position laid down by Colonel A\'oodthorpe. Such a result, 

 which I confess surpassed my expectations, shows how accurate the method of 

 estimation can be made with great care and some experience. I should add that 

 during those three months I was able to look back from each summit to others 

 which I had passed a week or a fortnight previously, and thus had several 

 opportunities of checking my results. 



I had carried with me two of those chronometers (Leroy) known in the navy 

 under the name of torpedo-boat watches, but I soon gave up using them. I 

 found that in a rough and difficult country, where falls, immersions, and all 

 manner of accidents were of constant occurrence, it was next to impossible to 

 preserve watches from sudden shocks. Further, we daily experienced changes in 

 temperature of as much as 20°, which disturbed their rate of going, while the 

 practical impossibility of making sufficiently long and frequent halts to regulate 

 them, quickly convinced me of the futility of attempting to determine longitude by 

 the passage of time. 



As for occultations, I confess that I had not a single opportunity of observing 

 one under favourable conditions. My telescope was not of sufficient power to 

 allow me to observe clearly the occultations of stars of the fifth and seventh 

 magnitude, nor did the atmospheric state e^•er admit a chance of observing those 

 of the first magnitude, which, as is well known, is sufficiently rare elsewhere. 



567 



